📝 Align API docs with updated interface template

docs/api/async-runtime-supports-background-worker.md

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+---
+name: async-runtime-supports-background-worker
+group: api
+category: async
+update-time: 20260512
+description: Return whether the current backend provides native async background worker support.
+key-word:
+    - async
+    - runtime
+    - worker
+    - public
+---
+
+## Async-runtime-supports-background-worker
+
+Return a boolean telling callers whether the current backend provides native background worker semantics for `bitlogger_async`. This is the narrowest capability probe when only worker support matters.
+
+### Interface
+
+```moonbit
+pub fn async_runtime_supports_background_worker() -> Bool {}
+```
+
+#### input
+
+- `none` - No explicit arguments are required.
+
+#### output
+
+- `Bool` - `true` when native background worker semantics are available, otherwise `false`.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- `true` indicates native worker capability.
+- `false` indicates compatibility-mode behavior.
+- This helper is derived from backend-specific async runtime implementation choice.
+- Use it when an enum branch is unnecessary and a boolean capability check is enough.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need A Simple Capability Branch
+
+When logic only depends on worker availability:
+```moonbit
+if async_runtime_supports_background_worker() {
+  println("native worker available")
+}
+```
+
+In this example, callers avoid a more verbose mode match.
+
+#### When Add Diagnostics Labels
+
+When capability should be surfaced in diagnostics:
+```moonbit
+println(if async_runtime_supports_background_worker() { "worker" } else { "compat" })
+```
+
+In this example, a simple boolean can drive compact status output.
+
+### Error Case
+
+e.g.:
+- This API does not normally fail at runtime; it reflects compiled backend behavior.
+
+- If you need the exact mode name rather than a boolean, use `async_runtime_mode()` or `async_runtime_state()`.
+
+### Notes
+
+Notes are here.
+
+1. Use this helper for minimal capability checks.
+
+2. Prefer `async_runtime_state()` when you want the same information in a richer object.
+
+3. Prefer `AsyncLogger::state()` when logger-instance counters matter too.
+
+4. This helper is intentionally small and should stay cheap to call.